I believe the way the active "web" material is displaced throughout the shorts is what designates lateral from linear.

Every "linear" pair of shorts I have ever come across has webbing from the glutes to the backs of the knees (vertical banding), while "lateral" shorts typically don't include this (resulting in the banding/webbing running only across the glutes and down the outer thighs). I have a pair of lateral shorts (they're old but I still like them!) and so I'm basing this on personal experience and observation -- hope it helps!